Coalescence of micrometer-scale droplets is impacted by several parameters, including droplet size, viscosities of the two phases, droplet velocity, angle of approach, as well as interfacial tension and surfactant coverage. The thinning dynamics of films between coalescing droplets can be particularly complex in the presence of surfactants, due to the generation of Marangoni stresses and reduced film mobility. Here, a microfluidic hydrodynamic "Stokes" trap is used to gently steer and trap surfactant-laden micrometer-sized droplets at the center of a cross-slot. Water droplets are formed upstream of the cross-slot using a microfluidic T-junction, in heavy and light mineral oils and stabilized using SPAN 80, an oil-soluble surfactant. Incoming droplets are made to coalesce with the trapped droplet, yielding measurements of the film drainage time. Film drainage times are measured as a function of continuous phase viscosity, incoming droplet speed, trapped droplet size, and surfactant concentrations above and below the critical micelle concentration (CMC). As expected, systems with higher surfactant concentrations and slower incoming droplet speed exhibit longer film drainage times. At low surfactant concentrations, the drainage time is longer for the more viscous heavy mineral oil in the continuous phase, whereas at high surfactant concentrations, the dependence on continuous phase viscosity vanishes. Perhaps more surprisingly, larger droplets and high confinement also result in longer film drainage times, potentially due to deformation of the droplet interfaces. The results are used here to determine critical conditions for coalescence, including both an upper and a lower critical capillary number. Moreover, it is shown that induced surfactant concentration gradient effects enable coalescence events after the droplets had originally flocculated, at surfactant concentrations above the CMC. The microfluidic hydrodynamic trap provides new insights into the role of surfactants in film drainage and opens avenues for controlled coalescence studies at micrometer length scales and millisecond time scales.